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A non-primitive boundary integral formulation for modeling flow through composite porous channel

机译:非原始边界积分公式,用于模拟通过复合多孔通道的流动

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In this study, we develop a non-primitive boundary integral formulation (BIF) for modeling flow through composite porous channel. We consider a planar channel having two packings that are filled with fully saturated porous media. We assume that the two porous media are isotropic and homogeneous in nature, but with different permeabilities. Brinkman equation is used to model fluid flow through porous media. Stress-jump condition is utilized at the porous-porous interface to account the flow exchange due to two layers porous media. We present BIF for steady two-dimensional flow of a viscous incompressible fluid through a composite porous channel with two layers having different permeabilities (Brinkman-Brinkman problem). The BIF developed is in terms of non-primitive variables namely, stream-function and vorticity. In the limit of large permeability Brinkman equation approaches Stokes equation. Hence, in order to assert the accuracy of our BEM code, we have considered the corresponding Stokes-Brinkman system. We derive the Brinkman layer thickness for Brinkman-Brinkman system as a function of various flow parameters. It is observed that Darcy number, stress-jump coefficients and the thickness parameter have significant effect on the flow mechanics.
机译:在这项研究中,我们开发了一种非原始边界积分公式(BIF),用于模拟通过复合多孔通道的流动。我们考虑一个具有两个填充物的平面通道,这些填充物充满了完全饱和的多孔介质。我们假设这两种多孔介质本质上是各向同性的,但具有不同的渗透率。 Brinkman方程用于模拟通过多孔介质的流体流动。在多孔-多孔界面处利用应力跳跃条件来说明由于两层多孔介质而引起的流动交换。我们提出了BIF,用于通过复合多孔通道的粘性不可压缩流体的稳定二维流动,该复合多孔通道具有两层具有不同渗透率的层(Brinkman-Brinkman问题)。开发的BIF是基于非原始变量,即流函数和涡度。在大渗透率的极限中,Brinkman方程逼近Stokes方程。因此,为了断言我们的BEM代码的准确性,我们考虑了相应的Stokes-Brinkman系统。我们根据各种流量参数得出Brinkman-Brinkman系统的Brinkman层厚度。可以看出,达西数,应力跃变系数和厚度参数对流动力学有显着影响。

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